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ravel
Joined: 21 Apr 2006
Posts: 536
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 Posted: Sat Jan 19, 2008 3:03 pm Post subject: About APE |
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APE's are very rare in puzzles and hard to spot.
This one can be solved with an APE only, but i solved it with xy-wing, UR and a "useless" w-wing, that connects another pair.
| Code: | +-------+-------+-------+
| 1 . 2 | . 3 . | 4 . 5 |
| . . 6 | . . . | 7 . . |
| . . . | . 8 . | . . . |
+-------+-------+-------+
| . . . | 2 . 9 | . . . |
| . 4 5 | . . . | 6 9 . |
| . . . | 4 . 3 | . . . |
+-------+-------+-------+
| 3 . 1 | . 7 . | 2 . 4 |
| . . . | . 2 . | . . . |
| . . 9 | . . . | 5 . . |
+-------+-------+-------+
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This one is somewhat similar. After 2 wings an APE pops up (and another wing and UR is needed). Alternatively you can solve it with kite, wings and the UR - for me the easier way.
| Code: | +-------+-------+-------+
| 1 . 2 | . 3 . | 4 . 5 |
| . . 6 | . . . | 7 . . |
| . . . | . 8 . | . . . |
+-------+-------+-------+
| . . . | 2 . 9 | . . . |
| . 4 1 | . . . | 6 5 . |
| . . . | 5 . 6 | . . . |
+-------+-------+-------+
| 3 . 8 | . 2 . | 1 . 7 |
| . . . | . 9 . | . . . |
| . . 7 | . . . | 3 . . |
+-------+-------+-------+
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[Added:]Maybe this one by gsf is the best sample. A 5-cell APE after the x-wing solves it.
| Code: | . . . | . . . | . . .
. . 8 | . 7 . | 3 . .
. 4 . | 3 . 1 | . 9 .
------+-------+------
. . 9 | . 3 . | 6 . .
. 1 . | 2 6 7 | . 8 .
. . 4 | . 5 . | 2 . .
------+-------+------
. 2 . | 8 . 4 | . 6 .
. . 5 | . 9 . | 8 . .
. . . | . . . | . . . |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Jan 19, 2008 6:20 pm Post subject: |
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| Quote: | APE's are very rare in puzzles and hard to spot.
This one can be solved with an APE only, but i solved it with xy-wing, UR and a "useless" w-wing, that connects another pair.
| Code: |
+-------+-------+-------+
| 1 . 2 | . 3 . | 4 . 5 |
| . . 6 | . . . | 7 . . |
| . . . | . 8 . | . . . |
+-------+-------+-------+
| . . . | 2 . 9 | . . . |
| . 4 5 | . . . | 6 9 . |
| . . . | 4 . 3 | . . . |
+-------+-------+-------+
| 3 . 1 | . 7 . | 2 . 4 |
| . . . | . 2 . | . . . |
| . . 9 | . . . | 5 . . |
+-------+-------+-------+ |
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I can't solve it with anything. I've had one unhelpful Type 4 UR and can't get past this point, even with extended Medusa.
| Code: |
+----------------+-------------+----------------+
| 1 89 2 | 67 3 67 | 4 5 89 |
| 458 358 6 | 15 9 24 | 7 1238 128 |
| 4579 3579 347 | 15 8 24 | 39 1236 1269 |
+----------------+-------------+----------------+
| 678 1367 378 | 2 56 9 | 18 4 57 |
| 2 4 5 | 78 1 78 | 6 9 3 |
| 6789 1679 78 | 4 56 3 | 18 27 257 |
+----------------+-------------+----------------+
| 3 568 1 | 9 7 568 | 2 68 4 |
| 45678 5678 478 | 368 2 1568 | 39 13678 16789 |
| 678 2 9 | 368 4 168 | 5 13678 1678 |
+----------------+-------------+----------------+
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Play this puzzle online at the Daily Sudoku site |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sat Jan 19, 2008 7:07 pm Post subject: |
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There seems to be some box/line or quad missing in your position, Marty.
Plus, I doubt the 5 in r1c8
After basics I had:
| Code: |
+--------------------------+--------------------------+--------------------------+
| 1 9 2 | 67 3 67 | 4 8 5 |
| 48 38 6 | 5 9 24 | 7 23 1 |
| 457 357 347 | 1 8 24 | 9 23 6 |
+--------------------------+--------------------------+--------------------------+
| 68 1368 38 | 2 5 9 | 18 4 7 |
| 2 4 5 | 78 1 78 | 6 9 3 |
| 9 178 78 | 4 6 3 | 18 5 2 |
+--------------------------+--------------------------+--------------------------+
| 3 58 1 | 9 7 58 | 2 6 4 |
| 45678 5678 478 | 68 2 1568 | 3 17 9 |
| 67 2 9 | 3 4 16 | 5 17 8 |
+--------------------------+--------------------------+--------------------------+ |
The XY-wing pivot r4c1 removes 8 from r8c3.
edit 2156 GMT: The XY-wing pivot r4c1 removes 7 from r8c3.
After that it's xy-chains, but they solve the puzzle. And all of them have that 16-17 (r9c6-r9c8) link in them, part of the useless 67-16-17 xy wing that ravel mentioned.
For me, APE is truly a method if all else fails and I have never been able to find a successful exclusion on my own. I probably miss some APE-gene ...
Last edited by nataraj on Sat Jan 19, 2008 9:58 pm; edited 1 time in total |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Jan 19, 2008 7:42 pm Post subject: |
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Using W-wings:
After a UR and an XY-wing,
| Code: | +-------------------+-------------------+-------------------+
| 1 9 2 | 67 3 67 | 4 8 5 |
| 48 38# 6 | 5 9 24 | 7 23 1 |
| 457 357 347 | 1 8 24 | 9 23 6 |
+-------------------+-------------------+-------------------+
| 68@ 136 38# | 2 5 9 | 18 4 7 |
| 2 4 5 | 78 1 78 | 6 9 3 |
| 9 17 78 | 4 6 3 | 18 5 2 |
+-------------------+-------------------+-------------------+
| 3 58 1 | 9 7 58 | 2 6 4 |
| 45678 5678 48 | 68@ 2 1568 | 3 17 9 |
| 67 2 9 | 3 4 16 | 5 17 8 |
+-------------------+-------------------+-------------------+ |
The cells @ are a W-wing that takes out <8> in R8C1. You can exclude a few more candidates <8> by coloring from R4C1.
The previous move made a strong link on <8> in C1. The cells # are now a W-wing that takes out <3> in R3C3 and R4C2. Then you need one more XY-wing and the puzzle is solved.
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Jan 19, 2008 10:05 pm Post subject: |
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| Quote: | There seems to be some box/line or quad missing in your position, Marty.
Plus, I doubt the 5 in r1c8
After basics I had: |
I think I'd better take another shot at it. The difference in the grids after the basics is just ridiculous.
Thanks.
| Quote: | | Plus, I doubt the 5 in r1c8 |
You're right. I just noticed that I made an error in transcribing the grid.
Update: after the basics I used a Type 4 UR and an XY-Chain. Ravel, what are the details of the APE that can solve this? I had a potential one in box 4, but couldn't eliminate anything. |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Sat Jan 19, 2008 11:54 pm Post subject: |
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| keith wrote: | The cells @ are a W-wing that takes out <8> in R8C1. You can exclude a few more candidates <8> by coloring from R4C1.
The previous move made a strong link on <8> in C1. The cells # are now a W-wing that takes out <3> in R3C3 and R4C2. Then you need one more XY-wing and the puzzle is solved. |
Ah, nice, so i only thought, that it is useless to eliminate this 8 from r8c1.
| Code: | +---------------------+-------------------+-------------------+
| 1 9 2 | 67 3 67 | 4 8 5 |
|*48 38 6 | 5 9 24 | 7 23 1 |
| 457 357 3-47 | 1 8 24 | 9 23 6 |
+---------------------+-------------------+-------------------+
| 68# @136 38 | 2 5 9 | 18 4 7 |
| 2 4 5 | 78 1 78 | 6 9 3 |
| 9 17 78 | 4 6 3 | 18 5 2 |
+---------------------+-------------------+-------------------+
| 3 58 1 | 9 7 58 | 2 6 4 |
|-4567-8 @5678 *48 |#68 2 1568 | 3 17 9 |
| 67 2 9 | 3 4 16 | 5 17 8 |
+---------------------+-------------------+-------------------+
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What i did was to "transport" the 8's (one of the 68 must be 8 from the w-wing) to the 4's of the 48 cells, i.e. one of them must be 4. Thus i could eliminate 4 from r3c3 an r8c1.
Marty,
the APE is already in your grid in boxes 1 and 2, eliminating an 8. But i would never have spotted it by my own. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Jan 20, 2008 12:52 am Post subject: |
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| Quote: | Marty,
the APE is already in your grid in boxes 1 and 2, eliminating an 8. But i would never have spotted it by my own. |
In my grid? The grid that I posted that was in error? But regardless, I don't see it. This grid that you posted resembles what I had and there was a near APE on 136-68 in box 4.
| Code: | +---------------------+-------------------+-------------------+
| 1 9 2 | 67 3 67 | 4 8 5 |
|*48 38 6 | 5 9 24 | 7 23 1 |
| 457 357 3-47 | 1 8 24 | 9 23 6 |
+---------------------+-------------------+-------------------+
| 68# @136 38 | 2 5 9 | 18 4 7 |
| 2 4 5 | 78 1 78 | 6 9 3 |
| 9 17 78 | 4 6 3 | 18 5 2 |
+---------------------+-------------------+-------------------+
| 3 58 1 | 9 7 58 | 2 6 4 |
|-4567-8 @5678 *48 |#68 2 1568 | 3 17 9 |
| 67 2 9 | 3 4 16 | 5 17 8 |
+---------------------+-------------------+-------------------+ |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Sun Jan 20, 2008 2:09 am Post subject: |
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Marty,
i am very sorry, the APE was not in your grid (dont know, where i looked at, as i wrote it) and it is in boxes 1 and 4, not 1 and 2.
| Code: | +---------------------+-------------------+-------------------+
| 1 9 2 | 67 3 67 | 4 8 5 |
|@48 38 6 | 5 9 24 | 7 23 1 |
| 457 357 #347 | 1 8 24 | 9 23 6 |
+---------------------+-------------------+-------------------+
| 6-8 136 #38 | 2 5 9 | 18 4 7 |
| 2 4 5 | 78 1 78 | 6 9 3 |
| 9 17 #78 | 4 6 3 | 18 5 2 |
+---------------------+-------------------+-------------------+
| 3 58 1 | 9 7 58 | 2 6 4 |
| 45678 5678 48 | 68 2 1568 | 3 17 9 |
| 67 2 9 | 3 4 16 | 5 17 8 |
+---------------------+-------------------+-------------------+ |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Jan 20, 2008 2:16 am Post subject: |
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I give up, I just can't see an APE there.  |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sun Jan 20, 2008 4:40 am Post subject: |
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| Looks like an ALS to me: shared exclusive is <4>; shared common is <8>. I, too, will need the APE explained. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Jan 20, 2008 5:24 am Post subject: |
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All,
I did a search on APE, and was surprised to find my footsteps all over the discussion.
http://www.sudoku.com/boards/viewtopic.php?t=3882
As I now recall, Ruud proposed that APE was a missing method from the usual arsenal.
I did an analysis that showed APE is another (less general) form of XY, XYZ, and WXYZ-wings. In other words, APE makes one exclusion at a time, XY.. wings make multiple exclusions.
APE is a monkey that you should not worry about.
I welcome any example of an APE exclusion that is not an XY... wing.
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Jan 20, 2008 6:14 am Post subject: |
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| Quote: | APE is a monkey that you should not worry about.
I welcome any example of an APE exclusion that is not an XY... wing. |
Don't hold your breath waiting for that example from me. However, while I won't worry about APE, I think it's worth knowing for those occasions when one misses an XY-Wing, but might notice the APE which, in my opinion, is easy to spot, or at least easy to spot a potential APE. But one could certainly live without it, as it doesn't occur very often. |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Sun Jan 20, 2008 1:44 pm Post subject: |
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There seems to be some confusion about the definition of an APE, probably because in the first samples the 2 cells (X and Y), which were investigated, share a box and a row/column.
When you follow the thread Keith pointed to you will find examples, where the 2 cells dont share a unit. Those can lead to eliminations that cannot be done with (w)xy(z)-wings.
Here X and Y are 68 in r4c1 and 347 in r3c3. Each pair combination with 8 in r4c1 (83, 84. 87) is blocked by a pair, which sees both cells. So 8 can be eliminated from r4c1.
In any case APE is a subset of ALS xz, where beside of X and Y only bivalue cells are involved. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Jan 20, 2008 4:26 pm Post subject: |
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Keith,
The Sudopedia examples don't contain an XY-Wing
http://www.sudopedia.org/wiki/Aligned_Pair_Exclusion
This 68-469 example in box 9 doesn't either, but we might be splitting hairs, as it does contain an XYZ.
| Code: |
+----------------+---------------+------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+----------------+---------------+------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+----------------+---------------+------------+
| 46789 56789 46 | 1 3589 3578 | 68 2 469 |
| 46789 6789 3 | 269 289 278 | 1 489 5 |
| 1689 15689 2 | 569 4 58 | 3 7 69 |
+----------------+---------------+------------+
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Play this puzzle online at the Daily Sudoku site |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Jan 20, 2008 6:57 pm Post subject: |
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Marty,
My memory is not entirely clear, so my statements from yesterday may not be accurate.
I do recall spending a lot of time writing down and studying the possible patterns that lead to APE exclusions. I decided that there were other (better, for me) methods to do the same thing.
As I recall, the whole thing seemed a little backwards to me - pick an elimination, then see if you can find cells that make it. I'd rather look for a pattern, then figure out if it makes any eliminations.
I see that Wikipedia does say: | Quote: | | Many APE moves can also be replicated by the easier XY-Wing and XYZ-Wing techniques. |
Best wishes,
Keith |
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Sun Jan 20, 2008 7:44 pm Post subject: |
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Another nice puzzle. Ravel says: | Quote: | | What i did was to "transport" the 8's (one of the 68 must be 8 from the w-wing) to the 4's of the 48 cells, i.e. one of them must be 4. |
Nice logic. Named technique? |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Jan 20, 2008 8:33 pm Post subject: |
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| keith wrote: | Marty,
My memory is not entirely clear, so my statements from yesterday may not be accurate.
I do recall spending a lot of time writing down and studying the possible patterns that lead to APE exclusions. I decided that there were other (better, for me) methods to do the same thing.
As I recall, the whole thing seemed a little backwards to me - pick an elimination, then see if you can find cells that make it. I'd rather look for a pattern, then figure out if it makes any eliminations.
I see that Wikipedia does say: | Quote: | | Many APE moves can also be replicated by the easier XY-Wing and XYZ-Wing techniques. |
Best wishes,
Keith |
I agree that many APEs are duplicative of XY/XYZ. But I don't necessarily go about solving puzzles with any rhyme or reason. I often start by looking for techniques that I enjoy and saving for last those which I don't enjoy (i.e., fish). I just learned APE about a month ago and it's still a novelty, so I'll look for them because I like to use newly learned techniques, even though it may not be the most efficient way to attack a puzzle. I've been on a Medusa kick lately and I used the most recent VH as Medusa practice, rather than solving it in the most direct manner. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Jan 20, 2008 11:27 pm Post subject: |
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| Victor wrote: | Another nice puzzle. Ravel says: | Quote: | | What i did was to "transport" the 8's (one of the 68 must be 8 from the w-wing) to the 4's of the 48 cells, i.e. one of them must be 4. |
Nice logic. Named technique? |
No name, just another example of the brilliant, creative things ravel seems to do all the time.
If you have seen Star Trek, "transport" seems about right. ravel magically puts things in a different place.
Keith |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Mon Jan 21, 2008 9:12 am Post subject: |
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| keith wrote: | | Victor wrote: | Another nice puzzle. Ravel says: | Quote: | | What i did was to "transport" the 8's (one of the 68 must be 8 from the w-wing) to the 4's of the 48 cells, i.e. one of them must be 4. |
Nice logic. Named technique? |
No name, just another example of the brilliant, creative things ravel seems to do all the time.
If you have seen Star Trek, "transport" seems about right. ravel magically puts things in a different place.
Keith |
Johan has done some transporting in some of his posts.
and I believe it was called "teleportation" in star strek, via an energy beam which broke down matter into a form of energy and put it all back together again in another place.
the device that did the teleportation was called a transporter.
so you are using the pincers of the (...choose your wing...) as the "transporter" and "teleporting" the candidates to make further eliminations.
however !!! the candidates are already there, so you aren't teleporting the candidates. you are teleporting the logic, relationship, connection...soul of the matter    
I think I just saw another "Jumper" movie ad...
Norm |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Mon Jan 21, 2008 11:29 am Post subject: |
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Keith,
have you looked at the (2nd and) 3rd puzzle? I cant identify this as a wing (though the 2 cells are in a box intersection) - [edit:] i saw now, its a case of wxyz-wing (r1c3 could be 1267 also - i knew it in a form with 12 instead of 27 or with 3-value cells).
| Code: | *-----------------------------------------------------*
|@36-79 3569 #126 | 569 4 256 |#17 #27 8 |
| 169 569 8 | 569 7 256 | 3 124 246 |
|#67 4 26 | 3 8 1 | 5-7 9 256-7 |
|-------------------+--------------+------------------|
| 2 7 9 | 4 3 8 | 6 5 1 |
| 5 1 3 | 2 6 7 | 49 8 49 |
| 68 68 4 | 1 5 9 | 2 37 37 |
|-------------------+--------------+------------------|
| 39 2 7 | 8 1 4 | 59 6 359 |
| 14 36 5 | 7 9 36 | 8 124 24 |
| 3489 389 16 | 56 2 356 | 1479 347 349 |
*-----------------------------------------------------*
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Btw i solved it with a 4-cell xy-chain + xy-wing. |
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